This is a Necessary Assumption question which we know because the question stem is asking us for an answer the argument relies on. This means the correct answer must be true if the argument is going to work, and if it isn’t true then the argument’s conclusion absolutely cannot follow.
Think about how significant a development this is in human history. Where would we be without math? And these simple counting tools are the earliest known evidence of its origins. Nice. Ok, but even though we had abstract representation of numbers as far back as 20,000 years, it was only 5,500 years ago that “systematic methods” were invented to write numbers. Okay, what about it? Well, since systematic methods only developed 5,500 years ago, conclusion: computation only became possible at that time.
I don’t really know what a “systematic method” is here, or how it differentiates from simple tally marks, but I suppose this makes sense. Ever tried to do basic division using Roman numerals? Good luck. And even Roman numerals could qualify as a systematic method since they are within our 5,500 year timeframe. Anything even worse than that and I guess I can see how calculations would be out of the question.
It’s very likely a correct answer will need to preclude more basic, non-systematic methods of representing numbers from being able to perform calculations. If I plus I equals II is a calculation, then it seems perfectly reasonable to think these 20,000 year old counting sticks could be thought of as calculators. We don’t want to commit to searching for anything in particular, and we want to stay open to suggestion of other things we may not have realized could be necessary, but it is certainly okay here if we are expecting our answer to do something in this area.
Answer Choice (A) No, we’re not interested in challenging the origins of these tools. In fact, the stimulus does not seem to entertain any possibility that these things aren’t exactly what we think they are. This certainly has nothing to do with our conclusion, in any case, and doesn’t have to be true for the conclusion to follow.
Answer Choice (B) Well I would think this would be true. I mean, we’re literally talking about rocks here. I very much doubt every last type of rock, bone, or stick was used. But even if this is almost certainly true, it doesn’t absolutely have to be true. They could’ve marked up every stick, stone, and bone on the planet and it would still have nothing to do with whether or not they were performing calculations.
Answer Choice (C) Well, yeah, but so what? They seem to date back 20,000 years. Homo sapiens evolved way longer ago than that. But, who cares? What if they do? So what? This has nothing to do with whether calculations were being performed before 5,500 years ago when “systematic methods” were invented.
Correct Answer Choice (D) Oh! This looks great. This establishes a “systematic method” of representation as a requirement for any computation. Whatever a “systematic method” is and whyever these earlier number symbols don’t qualify as systematic, we know there were no systematic methods until 5,500 years ago. This must be true for the conclusion to follow.
Answer Choice (E) We don’t care why it was invented, only when. Maybe they were invented just for the pure fun and joy of it. If so, not a problem at all.
We know this is a resolve reconcile explain question, because it asks: Which one of the following, if true, most helps to explain why the agricultural peoples of western Asia never returned to hunting and gathering?
The stimulus begins with some context; ten thousand years ago many of the communities in Western Asia switched from hunting and gathering to agriculture. Interestingly, this lead to poor diets and health issues, yet the people never returned to hunting and gathering. Our job is to explain why the communities stuck with agriculture when all we know so far is that it made their lives worse. A good answer choice will give a reason for their committal to agriculture that is compatible with the health effects mentioned in the stimulus. On to the answers:
Answer Choice (A) This doesn’t explain their committal to agriculture, it actually just makes the situation stranger by explicitly stating hunting and gathering food was still an option.
Answer Choice (B) Interesting! But this feature of both food methods doesn’t explain the committal to one over the other.
Correct Answer Choice (C) Here we go, this gives us a reason why hunting and gathering food just wasn’t going to cut it anymore, even if agriculture had negative trade offs. If one option isn’t going to work anymore, then sticking to the other makes sense.
Answer Choice (D) This tells us the phenomenon was widespread, but doesn’t provide an explanation for why it occurred in the first place.
Answer Choice (E) This just seems like another downside to agriculture, which makes the committal of the communities even less intelligible.
Here we have a resolve reconcile explain question, since it asks: Which one of the following, if true, most helps to resolve the apparent discrepancy?
Our stimulus begins by telling us that Mr. Young has the highest rate of unsuccessful collections at a collection agency. However, he is the best bill collector the agency has. The discrepancy is that we would expect a good bill collector to have less unsuccessful collections. We want to resolve this discrepancy by finding an answer choice which explains why Mr. Young might have a lot of unsuccessful collections in a way that is compatible with him being the best bill collector. Let’s see what we get!
Correct Answer Choice (A) This does exactly what we want! It would make sense that the hardest cases go to the best bill collector, and that the difficulty of these cases would lead to more unsuccessful collections.
Answer Choice (B) That’s very nice of the other bill collectors, but their opinions don’t do anything to explain why he has so many unsuccessful cases!
Answer Choice (C) Interesting! But again, his rate of collections remaining constant doesn’t explain a high rate of failed collections compared to others.
Answer Choice (D) Save it for his biography, this does nothing to help us!
Answer Choice (E) This just gives us another reason why we’d expect him to have a lower rate of unsuccessful collections compared to his juniors.
Here we have a strengthening questions, since the question stem demands: Which one of the following, if true, most strongly supports the conclusion drawn from the survey results?
The stimulus starts with the claim that financial success does not guarantee happiness. We should pause here and think about what a guarantee means. If something guarantees something else, then it is sufficient for something else. So what this first sentence really means is that it is not true that if you are financially successful then you are happy; financial success is not sufficient to produce happiness. The next sentence reveals the author’s position, as they assert that this claim has been verified by statistics. Interesting! Since this is a strengthening question, we want to anchor ourselves in this conclusion and get a good sense of what is supporting it. The final sentence introduces the support and tells us about a recent survey, where only one-third of respondents who claimed financial success also reported that they were happy.
If financial success did guarantee happiness, we would expect 100% of people with financial success to report that they are happy. The fact that only 33% did so is good evidence for our author’s conclusion. Unfortunately, there is just one problem. If we read the last sentence carefully, our sample for this statistic is composed of people who claimed to have financial success. Self-reporting should never inspire confidence. While there are many ways to strengthen this argument, we should be on the lookout for an answer that strengthens the connect between the respondents and being truly financially successful. Let’s see what the answers have in store for us:
Correct Answer Choice (A) This does exactly what we noticed the support needed. It strengthens the connection between our sample and actual financial success. If this is true, it guarantees there are at least some people who are financially successful and not happy, and therefore it is impossible that financial success is sufficient for happiness.
Answer Choice (B) We don’t care what people used to think or do think, nor whether financial success is necessary to happiness. Our conclusion is that, regardless of opinion, financial success is not sufficient for happiness.
Answer Choice (C) Financial security being sufficient for happiness wouldn’t mean that it is necessary to have financial security to be happy, so the existence of happy people without financial security isn’t strong support for our position. Even worse, this study still has the problem of self reporting.
Answer Choice (D) We are only told about what proportion of respondents who did report financial success were happy, we don’t know anything about the respondents who didn’t. Even if they were financially successful, maybe the all reported they were happy, in which case our argument would actually be weaker. Not enough information here.
Answer Choice (E) This would weaken our support by making a larger portion of those who reported financial success actually be happy.
We should recognize this is a strengthening question, since it asks: Which one of the following, if true, would most strengthen the argument?
Our stimulus begins by telling us that advertisers are often seen as unscrupulous (lacking restraint, essentially) in how they manipulate people’s desires. However, we’re then told that there is some evidence to the contrary; some advertisers are ethically motivated! That’s nice I guess, but I’m a bit skeptical; ‘ethical’ and ‘advertiser’ just don’t seem to go together often! Let’s see what evidence we have for this claim.
The argument cites a particular incidence where advertisers withdrew from a newspaper as it began to concentrate on sex and violence. Seems like the newspaper wants to profit from people’s desires! Our argument concludes the advertisers must have withdrew because they didn’t approve morally of the newspaper’s decision. This is the interpretation of the event which we want to support. What initially occurs to me is that it is entirely possible that the advertisers thought it would reflect badly on them if they were in the newspaper and could lose them money, and therefore their decision could have been entirely cynical. An answer choice which eliminates this alternate hypothesis that the advertisers were financially-motivated would be a good one. Let’s see what we get:
Answer Choice (A) Interesting, but this could be true if the advertisers withdrew for cynical reasons. This answer doesn’t give us enough information about the advertisers motives which is what we are interested in.
Answer Choice (B) We aren’t interested in those advertisers, we want to support a particular explanation of why some existing advertisers withdrew.
Correct Answer Choice (C) Bingo! If the advertisers knowingly took a haircut on their profits, that eliminates the alternate explanation that they did it all out of fear of losing money from not withdrawing.
Answer Choice (D) Ok? This, if anything, would lend support that the advertisers were motivated by financial rather than ethical considerations, and not strengthen our hypothesis.
Answer Choice (E) We don’t know whether this income group is poorer or richer and how that would affect the advertisers. Even if we did, how would it support our hypothesis that the advertisers withdrew because they were moral?
Here we have a MBT question, which we should recognize from the question stem: If the statements above are true, which one of the following must on the basis of them be true*?*
This question appears to be a lot more difficult than it really is; its difficulty lies in how dense with terminology the stimulus is. If we keep our cool, and focus on discerning the logical relations behind all this scientific jargon, we should have an easy time once we actually get to the answer choices. So don’t get lost in the noise, and make sure to anchor yourself in the conditionals and conjunctions as they show up.
Our first sentence tells us that these things called pyrrole molecules can combine to form polypyrroles. I don’t know about you, but I have never in my life heard of pyrrole molecules. Don’t let yourself be thrown off by this foreign language, what you should take away from this first sentence is that there are these things, pyrroles, and they can combine together. The next sentence continues with the weird language, bringing in this new thing, zeolites. As soon as we notice that the sentence begins with an if, we should look for a conditional relationship. The sentence gives us some information about polypyrrole combination when it is exposed to zeolite, and tells us there are two possible outcomes, conjoined by an OR that should jump at us. If we diagram this conditional, we should end up with something along the lines of: PP combination + Z → chains in Z or lumps on Z. So when we have these polypyrroles form near zeolite, they do so either in lumps on the zeolite, or chains within it. Interesting! The next sentence begins with the conditional indicator when, and we should once again use the logic to guide us through the language. It’s important to note in this conditional that the polypyrrole formation is the necessary condition, what triggers the rule. It’s not the case that polypyrrole formation is enough for the zeolite to change color, it is in fact required that if zeolite changes color from yellow to black, pyrrole formed either lumps on the zeolite or chains in it.
After all this explanation of polypyrrole formation and how it works around zeolites, we are given a phenomena; some yellow zeolite was submerged in pyrrole and turned black, without any pyrrole lumps forming. If we are pre-phrasing, we should recognize that we’ve been told pyrrole formation is required for zeolite to change from yellow to black, so it must have happened either in chains in the zeolite or in lumps on its surface. Since we are told there were no lumps, it must be true that the pyrrole formed chains in the zeolite. With this in mind, let’s look at the answer choices. As always on a MBT question, we should eliminate answers by considering whether it is possible for them to not be true given the information in the stimulus.
Answer Choice (A) This answer choice must be false, as we are explicitly told the zeolite was free of pyrroles before being submerged. If you selected this, you should work on reading the stimulus more carefully.
Answer Choice (B) B also must be false as we are told that no lumps formed on the zeolites surface after it had been submerged. Once again, you should be able to eliminate this answer quickly if you carefully read the stimulus.
Correct Answer Choice (C) This answer says exactly what we inferred in our pre-phrasing. Given the information in the stimulus, it is the only possible explanation for how the zeolite changed from yellow to black. Therefore, it must be true.
Answer Choice (D) Another answer choice that must be false. The third conditional the stimulus gives us requires that polypyrroles form if a zeolite changes from yellow to black. Since the zeolite was free of pyrrole before it was submerged, and changed from yellow to black after being submerged, there must have been some polypyrrole formation when it was submerged.
Answer Choice (E) This is the only incorrect answer choice that is not necessarily false. However, it is still not the case that it must be true. We are given no support to infer with certainty what quantity of the pyrrole entered the zeolites inner chamber.
We should recognize this as a must be true question, as the question stem states: If the statements above are true, which one of the following must also be true*?*
This stimulus is quite short for a MBT question. The first sentence tells us about the plan of an airport designed for private aircraft to cover its expenses by charging fees to private aircraft users. Unfortunately, the plan failed and the airport was unable to meet its expenses because the revenue from the fees was lower than expected. And that’s all we get! Since this is a MBT question, we know the correct answer is going to be a 100% guaranteed inference from just this information. The only thing we’ve really been told about is that the expenses were greater than both total revenue (superset) and specifically revenue from user fees (subset). The correct answer will have to somehow relate to this information. Let’s see what we get:
Answer Choice (A) We’ve been told nothing about where the county’s citizens live!
Answer Choice (B) The fact that there was any revenue from user fees strongly suggests this is at least partly false, and it certainly isn’t something we know for sure.
Answer Choice (C) This is just a total non sequitur, nothing was said about the airport’s construction.
Correct Answer Choice (D) If the airport was unable to pay its operating expenses, then its expenses must have been larger than its total revenue, and therefore it must be true that its expenses were greater than a subset of its total revenue.
Answer Choice (E) This requires a lot of assumptions as we know very little about the airport’s users.
This is a straight forward question stem for an NA question. The argument depends on the assumption in the answer. This is asking for necessity.
First off in this stimulus, that is a powerful sounding book. I don’t know of anything this convincing, so we’ve set a very extreme characteristic to this book. But remember that on the LSAT, we accept the assertions as true. So this book is all powerful in its persuasiveness. Members of the Earth Association gave away 2,000 copies last month. Given its persuasive power, that seems like a worthwhile thing to do for an environmental organization. “Thus” is introducing the conclusion here in the final line: The EA converted 2,000 people to the cause.
Well, a lot of problems might come to mind. First, it’s not enough for someone to own the book to be persuaded by it. It still needs to be read. Did any of these people they gave the books to read it? Also, to be converted, the recipients must not have already been environmentalists. Who are these people? The Earth Association better not have been distributing these at a convention for environmentalists, or I’m skeptical that they haven’t just been handing these out to people who were already environmentalists. Maybe these issues are obvious to some of us, maybe not to others. I do think these are particularly conspicuous compared to the average NA question, but we need not see these as problems. Whether you saw these or not, you still want to keep an open mind with the answer choices. There may very well be something else. With NA, there is almost always other directions a correct answer could take. For example, another NA here would be something like, “Copies of To Save the Earth are not printed in a font too small for any of the 2,000 recipients to read.” Bet no one predicted that, but it would be the right answer if provided. It goes to the same idea that each recipient actually read it, but its presented in a surprising way that may be difficult to recognize if we’re committed to looking for any answer in particular.
Answer Choice (A) Well that doesn’t have to be true. The more the merrier. We might have an issue if other organizations gave it to the same recipients, but this doesn’t say that. If it did, then these people would get this book with or without the Earth Association and so that could be a problem for their claim. If you selected this, did you think that’s what it said? Read carefully!
Answer Choice (B) This is wrong, but it’s a little tricky. Their “willingness” to buy it does not particularly matter. They could both be willing to buy it and not have bought it. I’d be willing to buy lots of things I have not actually bought. So just because they’d’ve been willing to buy it doesn’t mean they’d have obtained (and read) a copy. Furthermore, if they were willing to buy it, it doesn’t at all matter that they would have been willing to have bought it from the Earth Association. Any bookstore or online retailer or yard sale or anything else would be fine. This just doesn’t have to be true.
Answer Choice (C) Recycled paper? No. We might expect this book to be sustainably printed, but this has nothing to do with its persuasive power or whether or not the Earth Association has changed hearts and minds.
Correct Answer Choice (D) Here it is. If someone was already committed to the cause when the Earth Association gave them the book, then the Earth Association cannot claim to have converted that person to the cause they were already committed to.
Answer Choice (E) This is another slippery one. We do need each recipient to convert to the environmentalist cause, but that need not mean they embrace the specific brand of environmentalism advocated for by the Earth Association. That is an additional assumption which we are not at liberty to make and which prevents this answer from being necessary.